2.2. Binary addition

Adding binary numbers is a very simple task, and very similar to the longhand
addition of decimal numbers. As with decimal numbers, you start by adding the
bits (digits) one column, or place weight, at a time, from right to left. Unlike
decimal addition, there is little to memorize in the way of rules for the
addition of binary bits:

0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 10
1 + 1 + 1 = 11

Just as with decimal addition, when the sum in one column is a two-bit
(two-digit) number, the least significant figure is written as part of the total
sum and the most significant figure is "carried" to the next left column.
Consider the following examples:

The addition problem on the left did not require any bits to be carried,
since the sum of bits in each column was either 1 or 0, not 10 or 11. In the
other two problems, there definitely were bits to be carried, but the process of
addition is still quite simple.

As we'll see later, there are ways that electronic circuits can be built to
perform this very task of addition, by representing each bit of each binary
number as a voltage signal (either "high," for a 1; or "low" for a 0). This is
the very foundation of all the arithmetic which modern digital computers
perform.